Fishbreath. Use only if you can say it lovingly enough to distract from its actual meaning.

We've obviously got a lot of work to do.

The good people at rinkworks.com have the following suggestion for making romantic pet names:

Mix up the syllables "pook," "wee," "hon," "oop," and "ums," (never use the syllables "skuzz" or "elch"), rhyme a lot, and make liberal references to baked goods. [...] "Sweetie Pumpkin Pookums" is a perfectly acceptable and effective pet name, as are "Moopsie Cutie," "Hunny Wunny Cakes," and, for the extravagant, "Snookie Wookum Weetie Bunny Pie." (It may seem odd to novices that cooked rodents would be romantic, but they are.)

French pet names

If you can do the accent, pretty much any phrase in French sounds
like a great nickname. Just start with "mon petit" / "ma petite"
("my little", masculine and feminine form respectively), and add
basically anything you find in a French dictionary. Some suggestions:

French word

Translation

Chou

Cabbage

Bien-aimée

Beloved

Chat/chaton

Cat/kitten

Cygne

Swan

Pantoufle

Slipper

Champignon

Mushroom

Baguette

Loaf of bread

Reader suggestions

Some good suggestions by readers:

Sweetie pootie pie. This is a classic, how did we miss it?

Pookalums. Ditto.

Happy-hips. Always a good thing, when hips are happy.

Sweet-sips. Happy hips are thirsty work.

Cuddle-cakes. Cuddling cakes would be a messy business, but
it does sound fun. And tasty.

Munchkin. This is making
me hungry. How about cuddle-cakes MacMunchkin?

Smooshie/mooshie. Ooshie is a good sound to end on.
Plooshie. Glooshie. Splooshie.

Honey bunny. Just wishin', and hoppin', and thinkin',
and prayin'...

Belle, Beau. I knew a cute cat called “Ma belle”
(my pretty one), but I annoyed its owner by calling it Mabel (a name
associated with great-aunts and grandmothers where I come from).
Luckily, not everyone is as much of a jerk as I am.

Snugglewuggles. Nothing says I love you like the -uggle
sound.

Hot cakes. Watch your hands don't get burnt.

Banana boat. Banana? Banana? Just what have bananas got
to do with... oh. Never mind.

Angel cake. Heavenly.

Grumblemoose. I don't quite understand why the idea of a big
lumbering brute muttering under its breath is appealing, but it
undoubtedly is.

Soapsud Sally. That's one slippery character.

Tigger toes. Like twinkle-toes, but with much more BOING.

Some extremely simple suggestions:

Princess. Works best for people you can imagine in
a frilly dress and a tiara, or for people you emphatically cannot
imagine dressed that way.

Beautiful. You can't go wrong with this one.

Calamity. Love can be disastrous. In a good way.

Some bizarre suggestions by readers:

Goat smuggler. Goat smuggling may sound romantic,
but believe me, it isn't. I'd like to see you try and hide a
goat under your shirt as the border patrol waves you over.

Swamp donkey. Swamp donkey? Seriously?

Muffin B*tt. Listen, insults can work as nicknames,
but only up to a point.

Ok, so there's just the one bizarre suggestion so far, but
it merited a list of its own. (update) Now there's a second one,
so the plural form has become accurate. Hooray for the internets!
(update) Three!

Do you have any suggestions?

Other resources

Rinkworks have a handy pet name generator to help you come up with a name for your... err... Wuggywoogledumpling.